TESTING/LIN/sqrt02.f(3) | Library Functions Manual | TESTING/LIN/sqrt02.f(3) |
NAME
TESTING/LIN/sqrt02.f
SYNOPSIS
Functions/Subroutines
subroutine sqrt02 (m, n, k, a, af, q, r, lda, tau, work,
lwork, rwork, result)
SQRT02
Function/Subroutine Documentation
subroutine sqrt02 (integer m, integer n, integer k, real, dimension( lda, * ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension( lda, * ) r, integer lda, real, dimension( * ) tau, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( * ) result)
SQRT02
Purpose:
SQRT02 tests SORGQR, which generates an m-by-n matrix Q with orthonormal columns that is defined as the product of k elementary reflectors. Given the QR factorization of an m-by-n matrix A, SQRT02 generates the orthogonal matrix Q defined by the factorization of the first k columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k), and checks that the columns of Q are orthonormal.
Parameters
M
M is INTEGER The number of rows of the matrix Q to be generated. M >= 0.
N
N is INTEGER The number of columns of the matrix Q to be generated. M >= N >= 0.
K
K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
A
A is REAL array, dimension (LDA,N) The m-by-n matrix A which was factorized by SQRT01.
AF
AF is REAL array, dimension (LDA,N) Details of the QR factorization of A, as returned by SGEQRF. See SGEQRF for further details.
Q
Q is REAL array, dimension (LDA,N)
R
R is REAL array, dimension (LDA,N)
LDA
LDA is INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= M.
TAU
TAU is REAL array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
WORK
WORK is REAL array, dimension (LWORK)
LWORK
LWORK is INTEGER The dimension of the array WORK.
RWORK
RWORK is REAL array, dimension (M)
RESULT
RESULT is REAL array, dimension (2) The test ratios: RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 133 of file sqrt02.f.
Author
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